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  Subjects -> ENGINEERING (Total: 2156 journals)
    - CHEMICAL ENGINEERING (186 journals)
    - CIVIL ENGINEERING (168 journals)
    - ELECTRICAL ENGINEERING (93 journals)
    - ENGINEERING (1164 journals)
    - ENGINEERING MECHANICS AND MATERIALS (355 journals)
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    - MECHANICAL ENGINEERING (81 journals)

ENGINEERING (1164 journals)            First | 4 5 6 7 8 9 10 11 | Last

Journal of Irrigation and Drainage Engineering     Full-text available via subscription   (Followers: 15)
Journal of K-Theory     Full-text available via subscription   (Followers: 1)
Journal of King Saud University - Engineering Sciences     Open Access  
Journal of Konbin     Open Access  
Journal of Liquid Chromatography & Related Technologies     Hybrid Journal   (Followers: 9)
Journal of Management in Engineering     Full-text available via subscription   (Followers: 10)
Journal of Manufacturing Science and Engineering     Full-text available via subscription   (Followers: 11)
Journal of Manufacturing Systems     Full-text available via subscription   (Followers: 6)
Journal of Manufacturing Technology Management     Hybrid Journal   (Followers: 4)
Journal of Mathematical Modelling and Algorithms     Hybrid Journal   (Followers: 2)
Journal of Mechatronics     Full-text available via subscription  
Journal of Membrane and Separation Technology     Hybrid Journal  
Journal of Metallurgy     Open Access   (Followers: 3)
Journal of Middle European Construction and Design of Cars     Open Access   (Followers: 1)
Journal of Molecular Catalysis B: Enzymatic     Hybrid Journal   (Followers: 1)
Journal of Motor Behavior     Hybrid Journal   (Followers: 9)
Journal of Multivariate Analysis     Hybrid Journal   (Followers: 6)
Journal of Nanoengineering and Nanomanufacturing     Full-text available via subscription   (Followers: 1)
Journal of Nanoparticle Research     Hybrid Journal   (Followers: 3)
Journal of Nanoscience     Open Access  
Journal of Nanoscience and Nanotechnology     Full-text available via subscription   (Followers: 12)
Journal of NanoScience, NanoEngineering & Applications     Full-text available via subscription  
Journal of Nanotechnology     Open Access   (Followers: 3)
Journal of Nanotechnology in Engineering and Medicine     Full-text available via subscription   (Followers: 6)
Journal of Natural Gas Science and Engineering     Hybrid Journal   (Followers: 3)
Journal of Near Infrared Spectroscopy     Full-text available via subscription   (Followers: 7)
Journal of Networks     Open Access   (Followers: 4)
Journal of Nonlinear Dynamics     Open Access  
Journal of Nuclear Engineering & Technology     Full-text available via subscription  
Journal of Ocean Engineering and Marine Energy     Hybrid Journal  
Journal of Oceanography and Marine Science     Open Access   (Followers: 2)
Journal of Operations Management     Hybrid Journal   (Followers: 19)
Journal of Optics     Hybrid Journal   (Followers: 2)
Journal of Optimization     Open Access  
Journal of Optoelectronics Engineering     Open Access  
Journal of Organizational Behavior     Hybrid Journal   (Followers: 32)
Journal of Petroleum Science Research     Open Access   (Followers: 1)
Journal of Phase Equilibria and Diffusion     Hybrid Journal   (Followers: 5)
Journal of Power Sources     Partially Free   (Followers: 31)
Journal of Pre-College Engineering Education Research     Open Access  
Journal of Pressure Vessel Technology     Full-text available via subscription   (Followers: 11)
Journal of Professional Issues in Engineering Education and Practice     Full-text available via subscription   (Followers: 6)
Journal of Quality and Reliability Engineering     Open Access   (Followers: 1)
Journal of Quality in Maintenance Engineering     Hybrid Journal   (Followers: 4)
Journal of Radiation Research and Applied Sciences     Open Access   (Followers: 1)
Journal of Rare Earths     Full-text available via subscription   (Followers: 2)
Journal of Real-Time Image Processing     Hybrid Journal   (Followers: 5)
Journal of Regional Science     Hybrid Journal   (Followers: 10)
Journal of Reinforced Plastics and Composites     Hybrid Journal   (Followers: 27)
Journal of Research of NIST     Open Access   (Followers: 1)
Journal of Research Updates in Polymer Science     Hybrid Journal  
Journal of Rock Mechanics and Geotechnical Engineering     Open Access   (Followers: 2)
Journal of Russian Laser Research     Hybrid Journal  
Journal of Safety Engineering     Open Access   (Followers: 5)
Journal of Safety Research     Hybrid Journal   (Followers: 19)
Journal of Science and Technology     Open Access  
Journal of Science and Technology (Ghana)     Open Access   (Followers: 2)
Journal of Science and Technology Policy Management     Hybrid Journal   (Followers: 2)
Journal of Scientific Computing     Hybrid Journal   (Followers: 3)
Journal of Scientific Innovations for Development     Open Access   (Followers: 2)
Journal of Semiconductors     Full-text available via subscription   (Followers: 2)
Journal of Sensor Technology     Open Access   (Followers: 3)
Journal of Shanghai Jiaotong University (Science)     Hybrid Journal  
Journal of Sol-Gel Science and Technology     Hybrid Journal   (Followers: 2)
Journal of Solar Energy     Open Access   (Followers: 5)
Journal of Solar Energy Engineering     Full-text available via subscription   (Followers: 16)
Journal of Superconductivity and Novel Magnetism     Partially Free   (Followers: 1)
Journal of Surface Investigation. X-ray, Synchrotron and Neutron Techniques     Hybrid Journal   (Followers: 2)
Journal of Surveying Engineering     Full-text available via subscription   (Followers: 7)
Journal of Technology Management & Innovation     Open Access   (Followers: 3)
Journal of Testing and Evaluation     Full-text available via subscription   (Followers: 16)
Journal of the Air & Waste Management Association     Hybrid Journal   (Followers: 3)
Journal of the Chinese Institute of Engineers     Hybrid Journal  
Journal of the Chinese Institute of Industrial Engineers     Hybrid Journal   (Followers: 1)
Journal of the Franklin Institute     Full-text available via subscription   (Followers: 2)
Journal of the Institution of Engineers (India ): Series D     Hybrid Journal  
Journal of the Institution of Engineers (India) : Series B     Hybrid Journal   (Followers: 1)
Journal of The Institution of Engineers (India) : Series E     Hybrid Journal   (Followers: 1)
Journal of the Institution of Engineers (India): Series A     Hybrid Journal  
Journal of the Institution of Engineers (India): Series C     Hybrid Journal   (Followers: 1)
Journal of the National Science Foundation of Sri Lanka     Open Access   (Followers: 1)
Journal of the University of Ruhuna     Open Access  
Journal of Thermal Science and Engineering Applications     Full-text available via subscription   (Followers: 3)
Journal of Thermal Stresses     Hybrid Journal   (Followers: 3)
Journal of Transplantation     Open Access   (Followers: 4)
Journal of Transport and Supply Chain Management     Open Access   (Followers: 6)
Journal of Transportation Engineering     Full-text available via subscription   (Followers: 14)
Journal of Transportation Systems Engineering and Information Technology     Full-text available via subscription   (Followers: 15)
Journal of Tribology     Full-text available via subscription   (Followers: 28)
Journal of Turbomachinery     Full-text available via subscription   (Followers: 11)
Journal of Turbulence     Hybrid Journal   (Followers: 1)
Journal of Unmanned Vehicle Systems     Full-text available via subscription   (Followers: 2)
Journal of Urban and Environmental Engineering     Open Access  
Journal of Urban Planning and Development     Full-text available via subscription   (Followers: 32)
Journal of Urban Regeneration & Renewal     Full-text available via subscription   (Followers: 17)
Journal of Vibration and Acoustics     Full-text available via subscription   (Followers: 28)
Journal of Visualization     Hybrid Journal   (Followers: 2)
Journal of Volcanology and Seismology     Hybrid Journal   (Followers: 3)
Journal of Wuhan University of Technology-Mater. Sci. Ed.     Hybrid Journal  
Journal of Zhejiang University SCIENCE A     Hybrid Journal  

  First | 4 5 6 7 8 9 10 11 | Last

Journal Cover   Physica D: Nonlinear Phenomena
  [SJR: 1.048]   [H-I: 89]   [3 followers]  Follow
    
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 0167-2789
   Published by Elsevier Homepage  [2812 journals]
  • Domain coarsening in a subdiffusive Allen–Cahn equation
    • Abstract: Publication date: Available online 26 June 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): M. Abu Hamed , A.A. Nepomnyashchy
      Domain coarsening in a one-dimensional bistable system governing by a subdiffusive generalization of the Allen–Cahn equation is considered. Integro-differential equations governing the motion of interacting domain walls are derived and solved analytically and numerically. The dependence of the domain wall dynamics on the subdiffusion parameter is investigated.


      PubDate: 2015-07-01T11:33:57Z
       
  • A multidomain model for ionic electrodiffusion and osmosis with an
           application to cortical spreading depression
    • Abstract: Publication date: Available online 29 June 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Yoichiro Mori
      Ionic electrodiffusion and osmotic water flow are central processes in many physiological systems. We formulate a system of partial differential equations that governs ion movement and water flow in biological tissue. A salient feature of this model is that it satisfies a free energy identity, ensuring the thermodynamic consistency of the model. A numerical scheme is developed for the model in one spatial dimension and is applied to a model of cortical spreading depression, a propagating breakdown of ionic and cell volume homeostasis in the brain.


      PubDate: 2015-07-01T11:33:57Z
       
  • Transitions between streamline topologies of structurally stable
           Hamiltonian flows in multiply connected domains
    • Abstract: Publication date: 1 July 2015
      Source:Physica D: Nonlinear Phenomena, Volume 307
      Author(s): Takashi Sakajo , Tomoo Yokoyama
      We consider Hamiltonian vector fields with a dipole singularity satisfying the slip boundary condition in two-dimensional multiply connected domains. One example of such Hamiltonian vector fields is an incompressible and inviscid flow in exterior multiply connected domains with a uniform flow, whose Hamiltonian is called the stream function. Here, we are concerned with topological structures of the level sets of the Hamiltonian, which we call streamlines by analogy from incompressible fluid flows. Classification of structurally stable streamline patterns has been considered in Yokoyama and Sakajo (2013), where a procedure to assign a unique sequence of words, called the maximal word, to these patterns is proposed. Thanks to this procedure, we can identify every streamline pattern with its representing sequence of words up to topological equivalence. In the present paper, based on the theory of word representations, we propose a combinatorial method to provide a list of possible transient structurally unstable streamline patterns between two different structurally stable patterns by simply comparing their maximal word representations without specifying any Hamiltonian. Although this method cannot deal with topological streamline changes induced by bifurcations, it reveals the existence of many non-trivial global transitions in a generic sense. We also demonstrate how the present theory is applied to fluid flow problems with vortex structures.


      PubDate: 2015-06-26T14:28:59Z
       
  • Stability of front solutions in a model for a surfactant driven flow on an
           inclined plane
    • Abstract: Publication date: 1 July 2015
      Source:Physica D: Nonlinear Phenomena, Volume 307
      Author(s): Anna Ghazaryan , Stéphane Lafortune , Vahagn Manukian
      We consider a model for the flow of a thin liquid film down an inclined plane in the presence of a surfactant. The model is known to possess various families of traveling wave solutions. We use a combination of analytical and numerical methods to study the stability of the traveling waves. We show that for at least some of these waves the spectra of the linearization of the system about them are within the closed left-half complex plane.


      PubDate: 2015-06-26T14:28:59Z
       
  • Adaptive bipartite consensus on coopetition networks
    • Abstract: Publication date: 1 July 2015
      Source:Physica D: Nonlinear Phenomena, Volume 307
      Author(s): Jiangping Hu , Hong Zhu
      In this paper, a bipartite consensus tracking problem is considered for a group of autonomous agents on a coopetition network, on which the agents interact cooperatively and competitively simultaneously. The coopetition network involves positive and negative edges and is conveniently modeled by a signed graph. Additionally, the dynamics of all the agents are subjected to unknown disturbances, which are represented by linearly parameterized models. An adaptive estimation scheme is designed for each agent by virtue of the relative position measurements and the relative velocity measurements from its neighbors. Then a consensus tracking law is proposed for a new distributed system, which uses the relative measurements as the new state variables. The convergence of the consensus tracking error and the parameter estimation are analyzed even when the coopetition network is time-varying and no more global information about the bounds of the unknown disturbances is available to all the agents. Finally, some simulation results are provided to demonstrate the formation of the bipartite consensus on the coopetition network.


      PubDate: 2015-06-26T14:28:59Z
       
  • Traveling wave profiles for a crystalline front invading liquid states:
           Analytical and numerical solutions
    • Abstract: Publication date: 15 July 2015
      Source:Physica D: Nonlinear Phenomena, Volume 308
      Author(s): P.K. Galenko , F. Iunes Sanches , K.R. Elder
      The properties of a two dimensional crystalline phase invading a metastable or unstable liquid state are examined using the amplitude expansion formulation of the hyperbolic and parabolic phase-field crystal model. When the amplitudes are real and equal to each other, analytic expressions are derived for the profile of a steady state liquid–solid front traveling at constant velocity. Numerical simulations of the full amplitude formulation are conducted and compared with the analytic results. Close to the melting transition the analytic results for the liquid–solid profile, velocity and width are in quantitative agreement with the numerical results and disagree far from the transition.


      PubDate: 2015-06-26T14:28:59Z
       
  • Phase field based nonlocal anisotropic damage mechanics model
    • Abstract: Publication date: 15 July 2015
      Source:Physica D: Nonlinear Phenomena, Volume 308
      Author(s): Navid Mozaffari , George Z. Voyiadjis
      A nonlocal anisotropic damage theory is developed in this work through the phase field method to address the anisotropic damage evolution in materials. The anisotropic damage is discussed and appropriate nonconserved order parameters in three mutually perpendicular directions are defined to find the growth of the components of a second order diagonal damage tensor corresponding to the principal directions of a general second order damage tensor. In contrast to the previous models, two new tensors are proposed to act as interpolation and potential functions along with the Allen–Cahn equation in order to obtain the evolution of the order parameters, which is the basis of the definition of the damage rate. The tensor formulation of the growth of the components of the damage tensor is proposed for the first time. It is shown that, by introducing a set of material parameters including a length scale parameter due to damage, there is a robust and simplified way to model the nonlocal behavior of damage and predict the corresponding material behavior as components of a second order diagonal damage tensor.


      PubDate: 2015-06-26T14:28:59Z
       
  • Star pentagon and many stable choreographic solutions of the Newtonian
           4-body problem
    • Abstract: Publication date: 1 July 2015
      Source:Physica D: Nonlinear Phenomena, Volume 307
      Author(s): Tiancheng Ouyang , Zhifu Xie
      In this paper, we give a rigorous proof of the existence of infinitely many simple choreographic solutions in the classical Newtonian 4-body problem. These orbits are discovered by a variational method with structural prescribed boundary conditions (SPBC). This method provides an initial path that is obtained by minimizing the Lagrangian action functional over the SPBC. We prove that the initial path can be extended to a periodic or quasi-periodic solution. With computer-assistance, a family of choreographic orbits of this type is shown to be linearly stable. Among the many linearly stable simple choreographic orbits, the most extraordinary one is the stable star pentagon choreographic solution. We also prove the existence of infinitely many double choreographic periodic solutions, infinitely many non-choreographic periodic solutions and uncountably many quasi-periodic solutions. Each type of periodic solutions has many stable solutions and possibly infinitely many stable solutions. Our results with SPBC largely complement the current results by minimizing the action on a loop space.


      PubDate: 2015-06-26T14:28:59Z
       
  • Dynamics and absorption properties of stochastic equations with
           Hölder diffusion coefficients
    • Abstract: Publication date: 1 July 2015
      Source:Physica D: Nonlinear Phenomena, Volume 307
      Author(s): Jonathan Touboul , Gilles Wainrib
      In this article, we characterize the dynamics and absorption properties of a class of stochastic differential equations around singular points where both the drift and diffusion functions vanish. According to the Hölder coefficient α of the diffusion function around the singular point, we identify different regimes: a regime where the solutions almost surely reach the singular point in finite time, and regimes of exponential attraction or repulsion from the singular point. Stability of the absorbing state, large deviations for the absorption time, existence of stationary or quasi-stationary distributions are discussed. In particular, we show that quasi-stationary distributions only exist for α < 3 / 4 , and for α ∈ ( 3 / 4 , 1 ) , no quasi-stationary distribution is found and numerical simulations tend to show that the process conditioned on not being absorbed initiates an almost sure exponential convergence towards the absorbing state (as is demonstrated to be true for α = 1 ). These results have several implications in the understanding of stochastic bifurcations, and we completely unfold two generic situations: the pitchfork and saddle–node bifurcations, and discuss the Hopf bifurcation in the appendix.


      PubDate: 2015-06-26T14:28:59Z
       
  • Two-dimensional expansion of a condensed dense Bose gas
    • Abstract: Publication date: 1 July 2015
      Source:Physica D: Nonlinear Phenomena, Volume 307
      Author(s): E.S. Annibale , A. Gammal , K. Ziegler
      We study the expansion dynamics of a condensate in a strongly interacting Bose gas in the presence of an obstacle. Our focus is on the generation of shock waves after the Bose gas has passed the obstacle. The strongly interacting Bose gas is described in the slave-boson representation. A saddle-point approximation provides a nonlinear equation of motion for the macroscopic wave function, analogous to the Gross–Pitaevskii equation of a weakly interacting Bose gas but with different nonlinearity. We compare the results with the Gross–Pitaevskii dynamics of a weakly interacting Bose gas and find a similar behavior with a slower behavior of the strongly interacting system.


      PubDate: 2015-06-26T14:28:59Z
       
  • Dynamical Hamiltonian–Hopf instabilities of periodic traveling waves
           in Klein–Gordon equations
    • Abstract: Publication date: Available online 25 June 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): R. Marangell , P.D. Miller
      We study the unstable spectrum close to the imaginary axis for the linearization of the nonlinear Klein–Gordon equation about a periodic traveling wave in a co-moving frame. We define dynamical Hamiltonian–Hopf instabilities as points in the stable spectrum that are accumulation points for unstable spectrum, and show how they can be determined from the knowledge of the discriminant of an associated Hill’s equation. This result allows us to give simple criteria for the existence of dynamical Hamiltonian–Hopf instabilities in terms of instability indices previously shown to be useful in stability analysis of periodic traveling waves. We also discuss how these methods can be applied to more general nonlinear wave equations.


      PubDate: 2015-06-26T14:28:59Z
       
  • On Slater’s criterion for the breakup of invariant curves
    • Abstract: Publication date: Available online 24 June 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): C.V. Abud , I.L. Caldas
      We numerically explore Slater’s theorem in the context of dynamical systems to study the breakup of invariant curves. Slater’s theorem states that an irrational translation over a circle returns to an arbitrary interval in at most three different recurrence times expressible by the continued fraction expansion of the related irrational number. The hypothesis considered in this paper is that Slater’s theorem can be also verified in the dynamics of invariant curves. Hence, we use Slater’s theorem to develop a qualitative and quantitative numerical approach to determine the breakup of invariant curves in the phase space of area-preserving maps.


      PubDate: 2015-06-26T14:28:59Z
       
  • Extreme phase sensitivity in systems with fractal isochrons
    • Abstract: Publication date: Available online 19 June 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): A. Mauroy , I. Mezić
      Sensitivity to initial conditions is usually associated with chaotic dynamics and strange attractors. However, even systems with (quasi)periodic dynamics can exhibit it. In this context we report on the fractal properties of the isochrons of some continuous-time asymptotically periodic systems. We define a global measure of phase sensitivity that we call the phase sensitivity coefficient and show that it is an invariant of the system related to the capacity dimension of the isochrons. Similar results are also obtained with discrete-time systems. As an illustration of the framework, we compute the phase sensitivity coefficient for popular models of bursting neurons, suggesting that some elliptic bursting neurons are characterized by isochrons of high fractal dimensions and exhibit a very sensitive (unreliable) phase response.


      PubDate: 2015-06-26T14:28:59Z
       
  • Canalization and the stability of NK-Kauffman networks
    • Abstract: Publication date: 15 June 2015
      Source:Physica D: Nonlinear Phenomena, Volume 306
      Author(s): Federico Zertuche
      Boolean variables are such that they take values on Z 2 ≅ { 0 , 1 } . NK-Kauffman networks are dynamical deterministic systems of N Boolean functions that depend only on K ≤ N Boolean variables. They were proposed by Kauffman as a first step to understand cellular behavior (Kauffman, 1969) with great success. Among the problems that still have not been well understood in Kauffman networks, is the mechanism that regulates the phase transition of the system from an ordered phase where small changes of the initial state decay, to a chaotic one, where they grow exponentially. I show, that this mechanism is regulated through the irreducible decomposition of Boolean functions proposed in Zertuche (2009). This is in contrast to previous knowledge that attributed it to canalization. I also review other statistical properties of Kauffman networks that Boolean irreducibility explains.


      PubDate: 2015-06-26T14:28:59Z
       
  • Multistability and hidden attractors in a relay system with hysteresis
    • Abstract: Publication date: 15 June 2015
      Source:Physica D: Nonlinear Phenomena, Volume 306
      Author(s): Zhanybai T. Zhusubaliyev , Erik Mosekilde , Vasily G. Rubanov , Roman A. Nabokov
      For nonlinear dynamic systems with switching control, the concept of a “hidden attractor” naturally applies to a stable dynamic state that either (1) coexists with the stable switching cycle or (2), if the switching cycle is unstable, has a basin of attraction that does not intersect with the neighborhood of that cycle. We show how the equilibrium point of a relay system disappears in a boundary-equilibrium bifurcation as the system enters the region of autonomous switching dynamics and demonstrate experimentally how a relay system can exhibit large amplitude chaotic oscillations at high values of the supply voltage. By investigating a four-dimensional model of the experimental relay system we finally show how a variety of hidden periodic, quasiperiodic and chaotic attractors arise, transform and disappear through different bifurcations.


      PubDate: 2015-06-26T14:28:59Z
       
  • Partial classification of Lorenz knots: Syllable permutations of torus
           knots words
    • Abstract: Publication date: 15 June 2015
      Source:Physica D: Nonlinear Phenomena, Volume 306
      Author(s): Paulo Gomes , Nuno Franco , Luís Silva
      We define families of aperiodic words associated to Lorenz knots that arise naturally as syllable permutations of symbolic words corresponding to torus knots. An algorithm to construct symbolic words of satellite Lorenz knots is defined. We prove, subject to the validity of a previous conjecture, that Lorenz knots coded by some of these families of words are hyperbolic, by showing that they are neither satellites nor torus knots and making use of Thurston’s theorem. Infinite families of hyperbolic Lorenz knots are generated in this way, to our knowledge, for the first time. The techniques used can be generalized to study other families of Lorenz knots.


      PubDate: 2015-06-26T14:28:59Z
       
  • Bifurcations and strange nonchaotic attractors in a phase oscillator model
           of glacial–interglacial cycles
    • Abstract: Publication date: 15 June 2015
      Source:Physica D: Nonlinear Phenomena, Volume 306
      Author(s): Takahito Mitsui , Michel Crucifix , Kazuyuki Aihara
      Glacial–interglacial cycles are large variations in continental ice mass and greenhouse gases, which have dominated climate variability over the Quaternary. The dominant periodicity of the cycles is ∼ 40 kyr before the so-called middle Pleistocene transition between ∼ 1.2 and ∼ 0.7 Myr ago, and it is ∼ 100 kyr after the transition. In this paper, the dynamics of glacial–interglacial cycles are investigated using a phase oscillator model forced by the time-varying incoming solar radiation (insolation). We analyze the bifurcations of the system and show that strange nonchaotic attractors appear through nonsmooth saddle–node bifurcations of tori. The bifurcation analysis indicates that mode-locking is likely to occur for the 41 kyr glacial cycles but not likely for the 100 kyr glacial cycles. The sequence of mode-locked 41 kyr cycles is robust to small parameter changes. However, the sequence of 100 kyr glacial cycles can be sensitive to parameter changes when the system has a strange nonchaotic attractor.


      PubDate: 2015-06-26T14:28:59Z
       
  • On the backward behavior of some dissipative evolution equations
    • Abstract: Publication date: 15 June 2015
      Source:Physica D: Nonlinear Phenomena, Volume 306
      Author(s): Yanqiu Guo , Edriss S. Titi
      We prove that every solution of a KdV–Burgers–Sivashinsky type equation blows up in the energy space, backward in time, provided the solution does not belong to the global attractor. This is a phenomenon contrast to the backward behavior of the periodic 2D Navier–Stokes equations studied by Constantin et al. (1997), but analogous to the backward behavior of the Kuramoto–Sivashinsky equation discovered by Kukavica and Malcok (2005). Also we study the backward behavior of solutions to the damped driven nonlinear Schrödinger equation, the complex Ginzburg–Landau equation, and the hyperviscous Navier–Stokes equations. In addition, we provide some physical interpretation of various backward behaviors of several perturbations of the KdV equation by studying explicit cnoidal wave solutions. Furthermore, we discuss the connection between the backward behavior and the energy spectra of the solutions. The study of backward behavior of dissipative evolution equations is motivated by the investigation of the Bardos–Tartar conjecture on the Navier–Stokes equations stated in Bardos and Tartar (1973).


      PubDate: 2015-06-26T14:28:59Z
       
  • Phyllotaxis: Some progress, but a story far from over
    • Abstract: Publication date: 15 June 2015
      Source:Physica D: Nonlinear Phenomena, Volume 306
      Author(s): Matthew F. Pennybacker , Patrick D. Shipman , Alan C. Newell
      This is a review article with a point of view. We summarize the long history of the subject and recent advances and suggest that almost all features of the architecture of shoot apical meristems can be captured by pattern-forming systems which model the biochemistry and biophysics of those regions on plants.


      PubDate: 2015-06-26T14:28:59Z
       
  • Mobile localized solutions for an electron in lattices with dispersive and
           non-dispersive phonons
    • Abstract: Publication date: 15 June 2015
      Source:Physica D: Nonlinear Phenomena, Volume 306
      Author(s): Luis A. Cisneros-Ake , Leonor Cruzeiro , Manuel G. Velarde
      We consider a one dimensional lattice in which an electron can interact both with on-site non-dispersive (Einstein) phonons and with longitudinal dispersive acoustic (Debye) phonons. We provide existence conditions for mobile localized electron excitations in the long wave limit. The role of both types of phonon modes on localization is also assessed, together with a discussion of differences existing between the discrete and the continuum approaches. A striking result is that, under certain conditions, localized states can only be stable if they have a non-zero velocity.


      PubDate: 2015-06-26T14:28:59Z
       
  • Transport bounds for a truncated model of Rayleigh–Bénard
           convection
    • Abstract: Publication date: Available online 10 June 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Andre N. Souza , Charles R. Doering
      We investigate absolute limits on heat transport in a truncated model of Rayleigh–Bénard convection. Two complementary mathematical approaches—a background method analysis and an optimal control formulation—are used to derive upper bounds in a distinguished eight-ODE model proposed by Gluhovsky, Tong, and Agee. In the optimal control approach the flow no longer obeys an equation of motion, but is instead a control variable. Both methods produce the same estimate, but in contrast to the analogous result for the seminal three-ODE Lorenz system, the best upper bound apparently does not always correspond to an exact solution of the equations of motion.


      PubDate: 2015-06-26T14:28:59Z
       
  • On the motion of droplets driven by solutal Marangoni convection in alloy
           systems with a miscibility gap
    • Abstract: Publication date: Available online 9 June 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Fei Wang , Michael Selzer , Britta Nestler
      In the first part of this work, we analytically study the motion of two droplets driven by solutal Marangoni convection in a bipolar coordinate. Particular solutions for the Laplace and Stokes equations are found by applying Robin type boundary conditions for mass transfer and by utilizing continuity of stream function and impenetrability at the surface of droplets. The solutions for the Laplace and Stokes equations are connected by the tangential stress balance between the viscosity stress and the Marangoni stress caused by concentration gradients. In the second part, we numerically investigate the motion of two droplets in an immiscible fluid by solving the combined convective Cahn–Hilliard and Navier–Stokes equations, where the capillary tensor is used to account for the Marangoni force. A significant outcome of the present work is that the attraction or repulsion of droplets is determined by droplet radius and the Marangoni number. In both cases, we obtain the stream lines affected by the spacing between droplets and the ratio of the radius of the droplet.
      Graphical abstract image

      PubDate: 2015-06-26T14:28:59Z
       
  • Nonlinear conductance and heterogeneity of voltage-gated ion channels
           allow defining electrical surface domains in cell membranes
    • Abstract: Publication date: Available online 6 June 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Javier Cervera , José A. Manzanares , Salvador Mafe
      The membrane potential of a cell measured by typical electrophysiological methods is only an average magnitude and experimental techniques allowing a more detailed mapping of the cell surface have shown the existence of spatial domains with locally different electric potentials and currents. Electrical potentials in non-neural cells are regulated by the nonlinear conductance of membrane ion channels. Voltage-gated potassium channels participate in cell hyperpolarization/depolarization processes and control the electrical signals over the cell surface, constituting good candidates to study basic biological questions on a more simplified scale than the complex cell membrane. These channels show also a high heterogeneity, making it possible to analyze the effects of diversity in the electrical responses of channels localized on spatial domains. We use a phenomenological approach of voltage gating that reproduces the observed rectification characteristics of inward rectifying potassium channels and relate the threshold voltage heterogeneity of the channels to the establishment of spatial domains with different electrical sensitivities. Although our model is only a limited picture of the whole cell membrane, it shows that domains with different ion channels may permit or suppress steady state bioelectrical signals over the cell surface according to their particular voltage sensitivity. Also, the nonlinear electrical coupling of channels with different threshold potentials can lead to a rich variety of bioelectrical phenomena, including regions of membrane potential bi-stability.
      Graphical abstract image

      PubDate: 2015-06-26T14:28:59Z
       
  • Editorial Board
    • Abstract: Publication date: 1 June 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 304–305




      PubDate: 2015-06-26T14:28:59Z
       
  • Self-organized populations interacting under pursuit-evasion dynamics
    • Abstract: Publication date: 1 June 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 304–305
      Author(s): Thierry Goudon , Boniface Nkonga , Michel Rascle , Magali Ribot
      We discuss the modeling of interacting populations through pursuit-evasion–or attraction–repulsion–principles : preys try to escape chasers, chasers are attracted by the presence of preys. We construct a hierarchy of models, ranging from ODEs systems with finite numbers of individuals of each population, to hydrodynamic systems. First-order macroscopic models look like generalized “two-species Keller–Segel equations”. But, due to cross-interactions, we can show that the system does not exhibit any blow up phenomena in finite time. We also obtain second-order models, that have the form of systems of balance laws, derived from kinetic models. We bring out a few remarkable features of the models based either on mathematical analysis or numerical simulations.


      PubDate: 2015-06-26T14:28:59Z
       
  • Numerical study of the generalised Klein–Gordon equations
    • Abstract: Publication date: 1 June 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 304–305
      Author(s): Denys Dutykh , Marx Chhay , Didier Clamond
      In this study, we discuss an approximate set of equations describing water wave propagating in deep water. These generalised Klein–Gordon (gKG) equations possess a variational formulation, as well as a canonical Hamiltonian and multi-symplectic structures. Periodic travelling wave solutions are constructed numerically to high accuracy and compared to a seventh-order Stokes expansion of the full Euler equations. Then, we propose an efficient pseudo-spectral discretisation, which allows to assess the stability of travelling waves and localised wave packets.


      PubDate: 2015-06-26T14:28:59Z
       
  • Dynamics of erbium-doped fibre ring laser under cavity-loss modulation
    • Abstract: Publication date: 1 June 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 304–305
      Author(s): Gyanendra Kumar , R. Vijaya
      The time-domain response of an erbium doped fibre laser constructed with a uni-directional ring cavity is studied when the cavity loss is sinusoidally modulated in the frequency range of the relaxation oscillation frequency of the laser. Fourier transformed data are used to analyse the spectral features. The experimental demonstration of different periodic states and chaos thus reached under the period-doubling route at kHz frequencies are substantiated with numerical calculations using parameters appropriate to the experimental conditions. Bifurcation diagrams and reconstructed attractors are calculated to show the change of different dynamical regimes while varying the modulation frequency. The modulation of intra-cavity losses in a fibre laser enables the study of its nonlinear dynamical response in a highly controlled manner.


      PubDate: 2015-06-26T14:28:59Z
       
  • Synchronization of coupled chaotic maps
    • Abstract: Publication date: 1 June 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 304–305
      Author(s): Georgi S. Medvedev , Xuezhi Tang
      We prove a sufficient condition for synchronization for coupled one-dimensional maps and estimate the size of the window of parameters where synchronization takes place. It is shown that coupled systems on graphs with positive eigenvalues of the normalized graph Laplacian concentrated around 1 are more amenable for synchronization. In the light of this condition, we review spectral properties of Cayley, quasirandom, power-law graphs, and expanders and relate them to synchronization of the corresponding networks. The analysis of synchronization on these graphs is illustrated with numerical experiments. The results of this paper highlight the advantages of random connectivity for synchronization of coupled chaotic dynamical systems.


      PubDate: 2015-06-26T14:28:59Z
       
  • Numerical study of blow-up and dispersive shocks in solutions to
           generalized Korteweg–de Vries equations
    • Abstract: Publication date: 1 June 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 304–305
      Author(s): C. Klein , R. Peter
      We present a detailed numerical study of solutions to general Korteweg–de Vries equations with critical and supercritical nonlinearity, both in the context of dispersive shocks and blow-up. We study the stability of solitons and show that they are unstable against being radiated away and blow-up. In the L 2 critical case, the blow-up mechanism by Martel, Merle and Raphaël can be numerically identified. In the limit of small dispersion, it is shown that a dispersive shock always appears before an eventual blow-up. In the latter case, always the first soliton to appear will blow up. It is shown that the same type of blow-up as for the perturbations of the soliton can be observed which indicates that the theory by Martel, Merle and Raphaël is also applicable to initial data with a mass much larger than the soliton mass. We study the scaling of the blow-up time t ∗ in dependence of the small dispersion parameter ϵ and find an exponential dependence t ∗ ( ϵ ) and that there is a minimal blow-up time t 0 ∗ greater than the critical time of the corresponding Hopf solution for ϵ → 0 . To study the cases with blow-up in detail, we apply the first dynamic rescaling for generalized Korteweg–de Vries equations. This allows to identify the type of the singularity.


      PubDate: 2015-06-26T14:28:59Z
       
  • Editorial Board
    • Abstract: Publication date: 15 May 2015
      Source:Physica D: Nonlinear Phenomena, Volume 303




      PubDate: 2015-06-26T14:28:59Z
       
  • Signal amplification factor in stochastic resonance: An analytic
           non-perturbative approach
    • Abstract: Publication date: 15 May 2015
      Source:Physica D: Nonlinear Phenomena, Volume 303
      Author(s): Asish Kumar Dhara
      The response of an overdamped bistable system driven by a Gaussian white noise and perturbed by a weak monochromatic force (signal) is studied analytically. In order to get amplitude-dependent signal amplification factor a non-perturbative scheme is put forward by taking into account all the terms of a perturbation series with amplitude of the signal as an expansion parameter. An approximate analytic expression of the signal amplification factor is derived and compared with the numerical results. The contributions of infinite number of relaxation modes of the stochastic dynamics to the response are also taken into account in the final expression. The calculation of the response based on the derived expression requires only the knowledge of the first non-trivial eigenvalue and the lowest eigenfunction of the unperturbed Fokker–Planck operator.


      PubDate: 2015-06-26T14:28:59Z
       
  • Wave amplification in the framework of forced nonlinear Schrödinger
           equation: The rogue wave context
    • Abstract: Publication date: 15 May 2015
      Source:Physica D: Nonlinear Phenomena, Volume 303
      Author(s): Alexey Slunyaev , Anna Sergeeva , Efim Pelinovsky
      Irregular waves which experience the time-limited external forcing within the framework of the nonlinear Schrödinger (NLS) equation are studied numerically. It is shown that the adiabatically slow pumping (the time scale of forcing is much longer than the nonlinear time scale) results in selective enhancement of the solitary part of the wave ensemble. The slow forcing provides eventually wider wavenumber spectra, larger values of kurtosis and higher probability of large waves. In the opposite case of rapid forcing the nonlinear waves readjust passing through the stage of fast surges of statistical characteristics. Single forced envelope solitons are considered with the purpose to better identify the role of coherent wave groups. An approximate description on the basis of solutions of the integrable NLS equation is provided. Applicability of the Benjamin–Feir Index to forecasting of conditions favourable for rogue waves is discussed.


      PubDate: 2015-06-26T14:28:59Z
       
  • Synchronization of finite-state pulse-coupled oscillators
    • Abstract: Publication date: 15 May 2015
      Source:Physica D: Nonlinear Phenomena, Volume 303
      Author(s): Hanbaek Lyu
      We propose a novel generalized cellular automaton (GCA) model for discrete-time pulse-coupled oscillators and study the emergence of synchrony. Given a finite simple graph and an integer n ≥ 3 , each vertex is an identical oscillator of period n with the following weak coupling along the edges: each oscillator inhibits its phase update if it has at least one neighboring oscillator at a particular ”blinking” state and if its state is ahead of this blinking state. We obtain conditions on initial configurations and on network topologies for which states of all vertices eventually synchronize. We show that our GCA model synchronizes arbitrary initial configurations on paths, trees, and with random perturbation, any connected graph. In particular, our main result is the following local–global principle for tree networks: for n ∈ { 3 , 4 , 5 , 6 } , any n -periodic network on a tree synchronizes arbitrary initial configuration if and only if the maximum degree of the tree is less than the period n .


      PubDate: 2015-06-26T14:28:59Z
       
  • Transitions between symmetric and nonsymmetric regimes in binary-mixture
           convection
    • Abstract: Publication date: 15 May 2015
      Source:Physica D: Nonlinear Phenomena, Volume 303
      Author(s): Esteban Meca , Isabel Mercader , Laureano Ramírez-Piscina
      We present here a comprehensive picture of the different bifurcations found for small to moderate Rayleigh number in binary-mixture convection with lateral heating and negative separation ratio ( S ). The present work connects the symmetric regime found for pure fluid ( S = 0 ) (Mercader et al., 2005) with the fundamentally nonsymmetric regime found for S = − 1 (Meca et al., 2004) [2,3]. We give a global context as well as an interpretation for the different associations of bifurcations found, and in particular we interpret an association of codimension-two bifurcations in terms of a higher codimension bifurcation never found, to our knowledge, in the study of an extended system.


      PubDate: 2015-06-26T14:28:59Z
       
  • The Russo–Smereka kinetic equation: Conservation laws, reductions
           and numerical solutions
    • Abstract: Publication date: 15 May 2015
      Source:Physica D: Nonlinear Phenomena, Volume 303
      Author(s): Alexander A. Chesnokov , Maxim V. Pavlov
      The one-dimension Russo–Smereka kinetic equation describing the propagation of nonlinear concentration waves in a rarefied bubbly fluid is considered. Stability of the bubbly flow in terms of hyperbolicity of the kinetic equation is studied. It is proved that a hydrodynamical chain associated with the Russo–Smereka kinetic equation possesses infinitely many conservation laws. Reductions of the model to finite component systems are derived. Conservative form of the kinetic model is proposed and numerical solution of the Cauchy problem with discontinuous initial data is obtained.


      PubDate: 2015-06-26T14:28:59Z
       
  • Continuous data assimilation for the 2D Bénard convection through
           velocity measurements alone
    • Abstract: Publication date: 15 May 2015
      Source:Physica D: Nonlinear Phenomena, Volume 303
      Author(s): Aseel Farhat , Michael S. Jolly , Edriss S. Titi
      An algorithm for continuous data assimilation for the two-dimensional Bénard convection problem is introduced and analyzed. It is inspired by the data assimilation algorithm developed for the Navier–Stokes equations, which allows for the implementation of variety of observables: low Fourier modes, nodal values, finite volume averages, and finite elements. The novelty here is that the observed data is obtained for the velocity field alone; i.e. no temperature measurements are needed for this algorithm. We provide conditions on the spatial resolution of the observed data, under the assumption that the observed data is free of noise, which are sufficient to show that the solution of the algorithm approaches, at an exponential rate, the unique exact unknown solution of the Bénard convection problem associated with the observed (finite dimensional projection of) velocity.


      PubDate: 2015-06-26T14:28:59Z
       
  • Blow up Criterion of strong solution for 3D viscous liquid-gas two-phase
           flow model with vacuum
    • Abstract: Publication date: Available online 5 May 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Lili Du , Qin Zhang
      In this paper, we construct a blow-up criterion of the local strong solution to the three-dimensional (3D) viscous liquid-gas two-phase flow model only in terms of the divergence of the velocity field. Moreover, the initial vacuum is allowed, and there is no extra restriction on viscous coefficients. Both the Cauchy problem and initial–boundary value problem are considered in this paper.


      PubDate: 2015-06-26T14:28:59Z
       
  • Editorial Board
    • Abstract: Publication date: 1 May 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 301–302




      PubDate: 2015-06-26T14:28:59Z
       
  • Hamiltonian formulation of the extended Green–Naghdi equations
    • Abstract: Publication date: 1 May 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 301–302
      Author(s): Yoshimasa Matsuno
      A novel method is developed for extending the Green–Naghdi (GN) shallow-water model equation to the general system which incorporates the arbitrary higher-order dispersive effects. As an illustrative example, we derive a model equation which is accurate to the fourth power of the shallowness parameter while preserving the full nonlinearity of the GN equation, and obtain its solitary wave solutions by means of a singular perturbation analysis. We show that the extended GN equations have the same Hamiltonian structure as that of the GN equation. We also demonstrate that Zakharov’s Hamiltonian formulation of surface gravity waves is equivalent to that of the extended GN system by rewriting the former system in terms of the momentum density instead of the velocity potential at the free surface.


      PubDate: 2015-06-26T14:28:59Z
       
  • Nonlinear propagating localized modes in a 2D hexagonal crystal lattice
    • Abstract: Publication date: 1 May 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 301–302
      Author(s): Janis Bajars , J. Chris Eilbeck , Benedict Leimkuhler
      In this paper we consider a 2D hexagonal crystal lattice model first proposed by Marín, Eilbeck and Russell in 1998. We perform a detailed numerical study of nonlinear propagating localized modes, that is, propagating discrete breathers and kinks. The original model is extended to allow for arbitrary atomic interactions, and to allow atoms to travel out of the unit cell. A new on-site potential is considered with a periodic smooth function with hexagonal symmetry. We are able to confirm the existence of long-lived propagating discrete breathers. Our simulations show that, as they evolve, breathers appear to localize in frequency space, i.e. the energy moves from sidebands to a main frequency band. Our numerical findings shed light on the open question of whether exact moving breather solutions exist in 2D hexagonal layers in physical crystal lattices.


      PubDate: 2015-06-26T14:28:59Z
       
  • Exchange orbits in the planar 1+4 body problem
    • Abstract: Publication date: 1 May 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 301–302
      Author(s): A. Bengochea , J. Galán , E. Pérez-Chavela
      We study some doubly-symmetric orbits in the planar 1 + 2 n -body problem, that is the mass of the central body is significantly bigger than the other 2 n equal masses. The necessary and sufficient conditions for periodicity of the orbits are discussed. We also study numerically these kinds of orbits for the case n = 2 . The system under study corresponds to one conformed by a planet and four satellites of equal mass. We determine a 1 -parameter family of time-reversible invariant tori, related with the reversing symmetries of the equations of motion. The initial conditions of the orbits were determined by means of solving a boundary value problem with one free parameter. The numerical solution of the boundary value problem was obtained using the software AUTO. For the numerical analysis we have used the value of 3.5 × 1 0 − 4 as mass ratio of some satellite and the planet. In the computed solutions the satellites are in mean motion resonance 1:1 and they librate around a relative equilibria, that is a solution where the distances between the bodies remain constant for all time.


      PubDate: 2015-06-26T14:28:59Z
       
  • Controlling synchrony in a network of Kuramoto oscillators with
           time-varying coupling
    • Abstract: Publication date: 1 May 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 301–302
      Author(s): Rachel Leander , Suzanne Lenhart , Vladimir Protopopescu
      The Kuramoto model describes the synchronization of a heterogeneous population of oscillators through a stationary homogeneous network in which oscillators are coupled via their phase differences. Recently, there has been interest in studying synchronization on time-varying networks, and time-varying generalizations of the Kuramoto network, in particular. Previous results indicate that networks with fast dynamics may be as efficient as static networks at promoting synchrony. In this paper we use optimal control theory to study synchronization on a time-varying Kuramoto network. Our results indicate that time-varying networks can be more efficient than static networks at promoting synchrony and show that fast network dynamics are not necessary for efficiency. In particular, we show that, near the synchronization threshold, time-varying networks can promote synchrony through slow oscillations that lengthen the duration of high synchrony states and shorten the duration of low synchrony states. Interestingly, repulsion is an essential feature of these optimal dynamic networks.


      PubDate: 2015-06-26T14:28:59Z
       
  • The nonlinear interaction of convection modes in a box of a saturated
           porous medium
    • Abstract: Publication date: 1 May 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 301–302
      Author(s): Brendan J. Florio , Andrew P. Bassom , Neville Fowkes , Kevin Judd , Thomas Stemler
      A plethora of convection modes may occur within a confined box of porous medium when the associated dimensionless Rayleigh number R is above some critical value dependent on the geometry. In many cases the crucial Rayleigh number R c for onset is different for each mode, and in practice the mode with the lowest associated R c is likely to be the dominant one. For particular sizes of box, however, it is possible for multiple modes (typically three) to share a common R c . For box shapes close to these special geometries the modes interact and compete nonlinearly near the onset of convection. Here this mechanism is explored and it is shown that generically the dynamics of the competition takes on one of two possible structures. A specific example of each is described, while the general properties of the system enables us to compare our results with some previous calculations for particular box dimensions.


      PubDate: 2015-06-26T14:28:59Z
       
  • Elliptical optical solitary waves in a finite nematic liquid crystal cell
    • Abstract: Publication date: 1 May 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 301–302
      Author(s): Antonmaria A. Minzoni , Luke W. Sciberras , Noel F. Smyth , Annette L. Worthy
      The addition of orbital angular momentum has been previously shown to stabilise beams of elliptic cross-section. In this article the evolution of such elliptical beams is explored through the use of an approximate methodology based on modulation theory. An approximate method is used as the equations that govern the optical system have no known exact solitary wave solution. This study brings to light two distinct phases in the evolution of a beam carrying orbital angular momentum. The two phases are determined by the shedding of radiation in the form of mass loss and angular momentum loss. The first phase is dominated by the shedding of angular momentum loss through spiral waves. The second phase is dominated by diffractive radiation loss which drives the elliptical solitary wave to a steady state. In addition to modulation theory, the “chirp” variational method is also used to study this evolution. Due to the significant role radiation loss plays in the evolution of an elliptical solitary wave, an attempt is made to couple radiation loss to the chirp variational method. This attempt furthers understanding as to why radiation loss cannot be coupled to the chirp method. The basic reason for this is that there is no consistent manner to match the chirp trial function to the generated radiating waves which is uniformly valid in time. Finally, full numerical solutions of the governing equations are compared with solutions obtained using the various variational approximations, with the best agreement achieved with modulation theory due to its ability to include both mass and angular momentum losses to shed diffractive radiation.


      PubDate: 2015-06-26T14:28:59Z
       
  • Derivation of a wave kinetic equation from the resonant-averaged
           stochastic NLS equation
    • Abstract: Publication date: Available online 22 April 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Sergei Kuksin , Alberto Maiocchi
      We suggest a new derivation of a wave kinetic equation for the spectrum of the weakly nonlinear Schrödinger equation with stochastic forcing. The kinetic equation is obtained as a result of a double limiting procedure. Firstly, we consider the equation on a finite box with periodic boundary conditions and send the size of the nonlinearity and of the forcing to zero, while the time is correspondingly rescaled; then, the size of the box is sent to infinity (with a suitable rescaling of the solution). We report here the results of the first limiting procedure, analysed with full rigour in Kuksin and Maiocchi (0000), and show how the second limit leads to a kinetic equation for the spectrum, if some further hypotheses (commonly employed in the weak turbulence theory) are accepted. Finally we show how to derive from these equations the Kolmogorov-Zakharov spectra.


      PubDate: 2015-06-26T14:28:59Z
       
  • Editorial Board
    • Abstract: Publication date: 15 April 2015
      Source:Physica D: Nonlinear Phenomena, Volume 300




      PubDate: 2015-06-26T14:28:59Z
       
  • Kadomtsev–Petviashvili II equation: Structure of asymptotic soliton
           webs
    • Abstract: Publication date: 15 April 2015
      Source:Physica D: Nonlinear Phenomena, Volume 300
      Author(s): Shai Horowitz , Yair Zarmi
      A wealth of observations, recently supported by rigorous analysis, indicate that, asymptotically in time, most multi-soliton solutions of the Kadomtsev–Petviashvili II equation self-organize in webs comprised of solitons and soliton-junctions. Junctions are connected in pairs, each pair—by a single soliton. The webs expand in time. As distances between junctions grow, the memory of the structure of junctions in a connected pair ceases to affect the structure of either junction. As a result, every junction propagates at a constant velocity, which is determined by the wave numbers that go into its construction. One immediate consequence of this characteristic is that asymptotic webs preserve their morphology as they expand in time. Another consequence, based on simple geometric considerations, explains why, except in special cases, only 3-junctions (“ Y -shaped”, involving three wave numbers) and 4-junctions (“ X -shaped”, involving four wave numbers) can partake in the construction of an asymptotic soliton web.


      PubDate: 2015-06-26T14:28:59Z
       
  • Considerations on conserved quantities and boundary conditions of the
           2+1-dimensional nonlinear Schrödinger equation
    • Abstract: Publication date: 15 April 2015
      Source:Physica D: Nonlinear Phenomena, Volume 300
      Author(s): Javier Villarroel , Julia Prada
      In this study, we consider a natural integrable generalization of the defocusing cubic nonlinear Schrödinger equation to two dimensions and we classify the admissible boundary conditions. In particular, we determine whether the classical physical observables are conserved: mass, momentum, and Hamiltonian. We find that this is the case when a certain integral (the mass constraint) vanishes. The vanishing of the mass constraint, and thus the existence of conserved quantities, is contingent on the boundary conditions adopted. In particular, under decaying boundary conditions, the Hamiltonian is not necessarily conserved.


      PubDate: 2015-06-26T14:28:59Z
       
  • Modulational instabilities of periodic traveling waves in deep water
    • Abstract: Publication date: 15 April 2015
      Source:Physica D: Nonlinear Phenomena, Volume 300
      Author(s): Benjamin F. Akers
      The spectrum of periodic traveling waves in deep water is discussed. A multi-scale method is used, expanding the spectral data and the Bloch parameter in wave amplitude, to compute the size and location of modulated instabilities. The role of these instabilities in limiting the spectrum’s analyticity is explained. Both two-dimensional and three-dimensional instabilities are calculated. The asymptotic predictions are compared to numerical simulations.


      PubDate: 2015-06-26T14:28:59Z
       
  • (Non)Uniqueness of critical points in variational data assimilation
    • Abstract: Publication date: 15 April 2015
      Source:Physica D: Nonlinear Phenomena, Volume 300
      Author(s): Graham Cox
      In this paper we apply the 4D-Var data assimilation scheme to the initialization problem for a family of quasilinear evolution equations. The resulting variational problem is non-convex, so it need not have a unique minimizer. We comment on the implications of non-uniqueness for numerical applications, then prove uniqueness results in the following situations: (1) the observational times are sufficiently small; (2) the prior covariance is sufficiently small. We also give an example of a data set where the cost functional has a critical point of arbitrarily large Morse index, thus demonstrating that the geometry can be highly nonconvex even for a relatively mild nonlinearity.


      PubDate: 2015-06-26T14:28:59Z
       
 
 
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